We describe the observing strategy, data reduction tools and early results of a supernova (SN) search project, named SUDARE, conducted with the ESO VST telescope aimed at measuring the rate of the different types of SNe in the redshift range 0.2<z<0.8. The search was performed in two of the best-studied extragalactic fields, CDFS and COSMOS, for which a wealth of ancillary data are available in the literature or public archives. (abridged) We obtained a final sample of 117 SNe, most of which are SNIa (57%) and the remaining core collapse events of which 44% type II, 22% type IIn and 34% type Ib/c. In order to link the transients, we built a catalog of ~1.3x10^5 galaxies in the redshift range 0<z<1 with a limiting magnitude K_AB=23.5 mag. We measured the SN rate per unit volume for SN Ia and core collapse SNe in different bin of redshifts. The values are consistent with other measurements from the literature. The dispersion of the rate measurements for SNe Ia is comparable with the scatter of the theoretical tracks for single (SD) and double degenerate (DD) binary systems models, therefore the data do not allow to disentangle among the two different progenitor scenarios. However, we may notice that among the three tested models, SD and two flavours of DD, either with a steep (DDC) or a wide (DDW) delay time distribution, the SD gives a better fit across the whole redshift range whereas the DDC better matches the steep rise up to redshift ~1.2. The DDW appears instead less favoured. The core collapse SN rate is fully consistent, unlike recent claims, with the prediction based on recent estimates of the star formation history, and standard progenitor mass range.
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